improved Curl_fft, corrected Divergence_fft and added math_skew3x3
This commit is contained in:
Martin Diehl
parent
e7ac99eeca
commit
bd48620de2
169
code/math.f90
169
code/math.f90
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@ -563,7 +563,8 @@ real(pReal), dimension(4,36), parameter :: math_symOperations = &
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real(pReal), dimension(3), intent(in) :: B
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real(pReal), dimension(3) :: math_mul33x3
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forall (i=1_pInt:3_pInt) math_mul33x3(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3)
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!forall (i=1_pInt:3_pInt) math_mul33x3(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3)
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forall (i=1_pInt:3_pInt) math_mul33x3(i) = sum(A(i,1:3)*B(1:3))
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endfunction math_mul33x3
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@ -579,7 +580,7 @@ real(pReal), dimension(4,36), parameter :: math_symOperations = &
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real(pReal), dimension(3), intent(in) :: B
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complex(pReal), dimension(3) :: math_mul33x3_complex
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forall (i=1_pInt:3_pInt) math_mul33x3_complex(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3)
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forall (i=1_pInt:3_pInt) math_mul33x3_complex(i) = sum(A(i,1:3)*B(1:3))
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endfunction math_mul33x3_complex
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@ -1048,7 +1049,21 @@ pure function math_transpose3x3(A)
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endfunction math_symmetric6x6
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!********************************************************************
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! skew part of a 3x3 matrix
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!********************************************************************
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function math_skew3x3(m)
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implicit none
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real(pReal), dimension(3,3) :: math_skew3x3
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real(pReal), dimension(3,3), intent(in) :: m
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integer(pInt) :: i,j
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forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) math_skew3x3(i,j) = m(i,j) - 0.5_pReal * (m(i,j) + m(j,i))
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endfunction math_skew3x3
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!********************************************************************
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! equivalent scalar quantity of a full strain tensor
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!********************************************************************
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@ -2912,7 +2927,7 @@ end subroutine
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integer(pInt) i,j,k
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real(pReal) vol_initial
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Calculating volume mismatch'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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@ -2965,7 +2980,7 @@ subroutine shape_compare(res,geomdim,defgrad,nodes,centroids,shape_mismatch)
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real(pReal), dimension(8,3) :: coords_initial
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integer(pInt) i,j,k
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Calculating shape mismatch'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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@ -3053,7 +3068,8 @@ subroutine mesh_regular_grid(res,geomdim,defgrad_av,centroids,nodes)
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0_pInt, 1_pInt, 1_pInt &
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/), &
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(/3,8/))
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Meshing cubes around centroids'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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@ -3145,7 +3161,7 @@ subroutine deformed_linear(res,geomdim,defgrad_av,defgrad,coord_avgCorner)
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/), &
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(/3,6/))
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Restore geometry using linear integration'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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@ -3234,7 +3250,7 @@ subroutine deformed_fft(res,geomdim,defgrad_av,scaling,defgrad,coords)
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complex(pReal), parameter :: integration_factor = cmplx(0.0_pReal,pi*2.0_pReal)
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real(pReal), dimension(3) :: step, offset_coords
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Restore geometry using FFT-based integration'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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@ -3336,9 +3352,9 @@ subroutine curl_fft(res,geomdim,vec_tens,field,curl)
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integer(pInt) i, j, k, l, res1_red
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integer(pInt), dimension(3) :: k_s,cutting_freq
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real(pReal) :: wgt
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complex(pReal), parameter :: img = cmplx(0.0_pReal,1.0_pReal)
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complex(pReal), parameter :: differentation_factor = cmplx(0.0_pReal,1.0_pReal)*2.0_pReal*pi ! cmplx(0.0_pReal, 2.0_pReal*pi) gets huge rounding error (casting to single prec?)
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print*, 'Calculating curl of vector/tensor field'
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print '(a,e12.5,e12.5,e12.5)', ' Dimension: ', geomdim
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print '(a,i5,i5,i5)', ' Resolution:', res
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@ -3346,6 +3362,7 @@ subroutine curl_fft(res,geomdim,vec_tens,field,curl)
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wgt = 1.0_pReal/real(res(1)*res(2)*res(3),pReal)
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res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=102)
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call fftw_set_timelimit(fftw_timelimit)
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field_fftw = fftw_alloc_complex(int(res1_red *res(2)*res(3)*vec_tens*3_pInt,C_SIZE_T)) !C_SIZE_T is of type integer(8)
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@ -3382,38 +3399,23 @@ subroutine curl_fft(res,geomdim,vec_tens,field,curl)
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if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
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do i = 1, res1_red
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k_s(1) = i - 1_pInt
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xi(i,j,k,3) = real(k_s(3), pReal)/geomdim(3)
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xi(i,j,k,2) = real(k_s(2), pReal)/geomdim(2)
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xi(i,j,k,1) = real(k_s(1), pReal)/geomdim(1)
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xi(i,j,k,1:3) = real(k_s, pReal)/geomdim
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enddo; enddo; enddo
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!remove the given highest frequencies for calculation of the gamma operator
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!remove the given highest frequencies
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cutting_freq = (/0_pInt,0_pInt,0_pInt/) ! for 0,0,0, just the highest freq. is removed
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xi( res(1)/2_pInt+1_pInt-cutting_freq(1):res1_red , 1:res(2) , 1:res(3) , 1 ) = 0.0_pReal
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xi(1:res1_red , res(2)/2_pInt+1_pInt-cutting_freq(2):res(2)/2_pInt+1_pInt+cutting_freq(2) , 1:res(3) , 2) = 0.0_pReal
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xi(1:res1_red , 1:res(2) , res(3)/2_pInt+1_pInt-cutting_freq(3):res(3)/2_pInt+1_pInt+cutting_freq(3) , 3) = 0.0_pReal
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! do k = 1_pInt ,res(3); do j = 1_pInt ,res(2); do i = 1_pInt, res1_red
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! if((k > res(3)/2_pInt - cutting_freq(3)).and.(k <= res(3)/2_pInt + 1_pInt + cutting_freq(3))) xi(i,j,k,3) = 0.0_pReal
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! if((j > res(2)/2_pInt - cutting_freq(2)).and.(j <= res(2)/2_pInt + 1_pInt + cutting_freq(2))) xi(i,j,k,2) = 0.0_pReal
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! if((i > res(1)/2_pInt - cutting_freq(1)).and.(i <= res(1)/2_pInt + 1_pInt + cutting_freq(1))) xi(i,j,k,1) = 0.0_pReal
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! enddo; enddo; enddo
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curl_complex = 0.0_pReal
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do k = 1, res(3)
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do j = 1, res(2)
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do i = 1, res1_red
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do l = 1, vec_tens
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! curl_complex(i,j,k,l,1) = field_complex(i,j,k,l,1)
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! curl_complex(i,j,k,l,2) = field_complex(i,j,k,l,2)
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! curl_complex(i,j,k,l,3) = field_complex(i,j,k,l,3)
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curl_complex(i,j,k,l,1) = ( field_complex(i,j,k,l,3)*xi(i,j,k,2) - field_complex(i,j,k,l,2)*xi(i,j,k,3) )&
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*img*pi*2.0_pReal
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curl_complex(i,j,k,l,2) = (- field_complex(i,j,k,l,3)*xi(i,j,k,1) + field_complex(i,j,k,l,1)*xi(i,j,k,3) )&
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*img*pi*2.0_pReal
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curl_complex(i,j,k,l,3) = ( field_complex(i,j,k,l,2)*xi(i,j,k,1) - field_complex(i,j,k,l,1)*xi(i,j,k,2) )&
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*img*pi*2.0_pReal
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enddo
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do k = 1, res(3); do j = 1, res(2);do i = 1, res1_red
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do l = 1, vec_tens
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curl_complex(i,j,k,l,1) = ( field_complex(i,j,k,l,3)*xi(i,j,k,2)&
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-field_complex(i,j,k,l,2)*xi(i,j,k,3) )*differentation_factor
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curl_complex(i,j,k,l,2) = (-field_complex(i,j,k,l,3)*xi(i,j,k,1)&
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+field_complex(i,j,k,l,1)*xi(i,j,k,3) )*differentation_factor
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curl_complex(i,j,k,l,3) = ( field_complex(i,j,k,l,2)*xi(i,j,k,1)&
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-field_complex(i,j,k,l,1)*xi(i,j,k,2) )*differentation_factor
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enddo
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enddo; enddo; enddo
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call fftw_execute_dft_c2r(fftw_back, curl_complex, curl_real)
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@ -3452,28 +3454,32 @@ subroutine divergence_fft(res,geomdim,vec_tens,field,divergence)
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real(pReal), dimension(:,:,:,:), pointer :: divergence_real
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complex(pReal), dimension(:,:,:,:), pointer :: divergence_complex
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! other variables
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integer(pInt) :: i, j, k, res1_red
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complex(pReal), parameter :: img = cmplx(0.0_pReal,1.0_pReal)
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integer(pInt) :: i, j, k, l, res1_red
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real(pReal) :: wgt
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integer(pInt), dimension(3) :: k_s,cutting_freq
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complex(pReal), parameter :: differentation_factor = cmplx(0.0_pReal,1.0_pReal)*2.0_pReal*pi ! cmplx(0.0_pReal, 2.0_pReal*pi) gets huge rounding error (casting to single prec?)
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if (debug_verbosity > 0) then
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if (debug_verbosity > 0_pInt) then
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print '(a)', 'Calculating divergence of tensor/vector field using FFT'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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print '(a,/,i5,i5,i5)', ' Resolution:', res
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endif
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res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
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wgt = 1.0_pReal/real(res(1)*res(2)*res(3),pReal)
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if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=102)
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call fftw_set_timelimit(fftw_timelimit)
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field_fftw = fftw_alloc_complex(int(res1_red *res(2)*res(3)*vec_tens*3_pInt,C_SIZE_T)) !C_SIZE_T is of type integer(8)
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call c_f_pointer(field_fftw, field_real, [res(1)+2_pInt,res(2),res(3),3,vec_tens])
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call c_f_pointer(field_fftw, field_complex, [res1_red ,res(2),res(3),3,vec_tens])
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divergence_fftw = fftw_alloc_complex(int(res1_red *res(2)*res(3)*vec_tens,C_SIZE_T)) !C_SIZE_T is of type integer(8)
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field_fftw = fftw_alloc_complex(int(res1_red*res(2)*res(3)*vec_tens*3_pInt,C_SIZE_T)) !C_SIZE_T is of type integer(8)
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call c_f_pointer(field_fftw, field_real, [res(1)+2_pInt,res(2),res(3),vec_tens,3])
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call c_f_pointer(field_fftw, field_complex, [res1_red ,res(2),res(3),vec_tens,3])
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divergence_fftw = fftw_alloc_complex(int(res1_red*res(2)*res(3)*vec_tens,C_SIZE_T))
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call c_f_pointer(divergence_fftw, divergence_real, [res(1)+2_pInt,res(2),res(3),vec_tens])
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call c_f_pointer(divergence_fftw, divergence_complex,[res1_red ,res(2),res(3),vec_tens])
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fftw_forth = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),vec_tens*3_pInt,& ! dimensions , length in each dimension in reversed order
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field_real,(/res(3),res(2) ,res(1)+2_pInt/),& ! input data , physical length in each dimension in reversed order
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1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
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fftw_forth = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),vec_tens*3_pInt,& ! dimensions , length in each dimension in reversed order
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field_real,(/res(3),res(2) ,res(1)+2_pInt/),& ! input data , physical length in each dimension in reversed order
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1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
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field_complex,(/res(3),res(2) ,res1_red/),&
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1, res(3)*res(2)* res1_red,fftw_planner_flag)
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@ -3482,61 +3488,42 @@ subroutine divergence_fft(res,geomdim,vec_tens,field,divergence)
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1, res(3)*res(2)* res1_red,&
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divergence_real,(/res(3),res(2) ,res(1)+2_pInt/),&
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1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
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field_real = 0.0_pReal ! padding
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
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field_real(i,j,k,1:3,1:vec_tens) = field(i,j,k,1:3,1:vec_tens) ! ensure that data is aligned properly (fftw_alloc)
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field_real(i,j,k,1:vec_tens,1:3) = field(i,j,k,1:vec_tens,1:3) ! ensure that data is aligned properly (fftw_alloc)
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enddo; enddo; enddo
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call fftw_execute_dft_r2c(fftw_forth, field_real, field_complex)
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! Alternative calculation of discrete frequencies k_s, ordered as in FFTW (wrap around)
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! do k = 0,res(3)/2 -1
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! do j = 0,res(2)/2 -1
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! do i = 0,res(1)/2 -1
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! xi(1+mod(res(1)-i,res(1)),1+mod(res(2)-j,res(2)),1+mod(res(3)-k,res(3)),:) = (/-i,-j,-k/)/geomdim
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! xi(1+i, 1+mod(res(2)-j,res(2)),1+mod(res(3)-k,res(3)),:) = (/ i,-j,-k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+j, 1+mod(res(3)-k,res(3)),:) = (/-i, j,-k/)/geomdim
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! xi(1+i, 1+j, 1+mod(res(3)-k,res(3)),:) = (/ i, j,-k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+mod(res(2)-j,res(2)),1+k, :) = (/-i,-j, k/)/geomdim
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! xi(1+i, 1+mod(res(2)-j,res(2)),1+k, :) = (/ i,-j, k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+j, 1+k, :) = (/-i, j, k/)/geomdim
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! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim
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! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+j, 1+k, :) = (/-i, j, k/)/geomdim
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! xi(1+i, 1+mod(res(2)-j,res(2)),1+k, :) = (/ i,-j, k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+mod(res(2)-j,res(2)),1+k, :) = (/-i,-j, k/)/geomdim
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! xi(1+i, 1+j, 1+mod(res(3)-k,res(3)),:) = (/ i, j,-k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+j, 1+mod(res(3)-k,res(3)),:) = (/-i, j,-k/)/geomdim
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! xi(1+i, 1+mod(res(2)-j,res(2)),1+mod(res(3)-k,res(3)),:) = (/ i,-j,-k/)/geomdim
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! xi(1+mod(res(1)-i,res(1)),1+mod(res(2)-j,res(2)),1+mod(res(3)-k,res(3)),:) = (/-i,-j,-k/)/geomdim
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! enddo; enddo; enddo
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do k = 0_pInt, res(3)-1_pInt
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do j = 0_pInt, res(2)-1_pInt
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do i = 0_pInt, res(1)/2_pInt
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xi(i+1_pInt,j+1_pInt,k+1_pInt,1:3) = (/real(i,pReal),real(j,pReal),real(k,pReal)/)/geomdim
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if(k==res(3)/2_pInt) xi(i+1_pInt,j+1_pInt,k+1_pInt,3)= 0.0_pReal ! set highest frequencies to zero
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if(j==res(2)/2_pInt) xi(i+1_pInt,j+1_pInt,k+1_pInt,2)= 0.0_pReal
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if(i==res(1)/2_pInt) xi(i+1_pInt,j+1_pInt,k+1_pInt,1)= 0.0_pReal
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do k = 1_pInt, res(3) ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
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k_s(3) = k - 1_pInt
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if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
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do j = 1_pInt, res(2)
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k_s(2) = j - 1_pInt
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if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
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do i = 1, res1_red
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k_s(1) = i - 1_pInt
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xi(i,j,k,1:3) = real(k_s, pReal)/geomdim
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enddo; enddo; enddo
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do k = 1_pInt, res(3)
|
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do j = 1_pInt, res(2)
|
||||
do i = 1_pInt, res1_red
|
||||
divergence_complex(i,j,k,1) = sum(field_complex(i,j,k,1:3,1)*xi(i,j,k,1:3)) !ToDo: check formula!!!
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if(vec_tens == 3_pInt) then
|
||||
divergence_complex(i,j,k,2) = sum(field_complex(i,j,k,1:3,2)*xi(i,j,k,1:3))
|
||||
divergence_complex(i,j,k,3) = sum(field_complex(i,j,k,1:3,3)*xi(i,j,k,1:3))
|
||||
endif
|
||||
|
||||
!remove the given highest frequencies
|
||||
cutting_freq = 0_pInt ! for 0,0,0, just the highest freq. is removed
|
||||
xi( res(1)/2_pInt+1_pInt-cutting_freq(1):res1_red , 1:res(2) , 1:res(3) , 1 ) = 0.0_pReal
|
||||
xi(1:res1_red , res(2)/2_pInt+1_pInt-cutting_freq(2):res(2)/2_pInt+1_pInt+cutting_freq(2) , 1:res(3) , 2) = 0.0_pReal
|
||||
xi(1:res1_red , 1:res(2) , res(3)/2_pInt+1_pInt-cutting_freq(3):res(3)/2_pInt+1_pInt+cutting_freq(3) , 3) = 0.0_pReal
|
||||
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
||||
do l = 1_pInt, vec_tens
|
||||
divergence_complex(i,j,k,l) = sum(field_complex(i,j,k,l,1:3)*xi(i,j,k,1:3))&
|
||||
*differentation_factor
|
||||
enddo
|
||||
enddo; enddo; enddo
|
||||
divergence_complex = divergence_complex*img*2.0_pReal*pi
|
||||
|
||||
call fftw_execute_dft_c2r(fftw_back, divergence_complex, divergence_real)
|
||||
|
||||
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
||||
divergence(i,j,k,1:vec_tens) = divergence_real(i,j,k,1:vec_tens) ! ensure that data is aligned properly (fftw_alloc)
|
||||
enddo; enddo; enddo
|
||||
! why not weighting the divergence field?
|
||||
|
||||
divergence = divergence * wgt
|
||||
|
||||
end subroutine divergence_fft
|
||||
|
||||
|
||||
|
|
@ -3565,7 +3552,7 @@ subroutine divergence_fft(res,geomdim,vec_tens,field,divergence)
|
|||
4.0_pReal/5.0_pReal,-1.0_pReal/ 5.0_pReal,4.0_pReal/105.0_pReal,-1.0_pReal/280.0_pReal/),&
|
||||
(/4,4/))
|
||||
|
||||
if (debug_verbosity > 0) then
|
||||
if (debug_verbosity > 0_pInt) then
|
||||
print*, 'Calculating divergence of tensor/vector field using FDM'
|
||||
print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
|
||||
print '(a,/,i5,i5,i5)', ' Resolution:', res
|
||||
|
|
|
|||
Loading…
Reference in New Issue